一、前言

        保險公司對個人投保時或根據歷史資料生成的模型來計算個人保費，那麼本次我們就以這個模型的求解過程為例來實踐下多元線性迴歸。

二、資料&簡單分析

        我們已經獲取到保險公司部分資料，檔名為insurance.csv，檔案內容如下。

        我們可以看出資料中共有六個維度：age（年齡）,sex（性別）,bmi（肥胖指數）,children（孩子數量）,smoker（是否吸菸）,region（居住地）。charges則是當前資料人上年度在醫院的花銷。

        所以我們可以構建一個六維高維空間來求解這個模型。

age,sex,bmi,children,smoker,region,charges
19,female,27.9,0,yes,southwest,16884.924
18,male,33.77,1,no,southeast,1725.5523
28,male,33,3,no,southeast,4449.462
33,male,22.705,0,no,northwest,21984.47061
32,male,28.88,0,no,northwest,3866.8552
31,female,25.74,0,no,southeast,3756.6216
46,female,33.44,1,no,southeast,8240.5896
37,female,27.74,3,no,northwest,7281.5056
37,male,29.83,2,no,northeast,6406.4107
60,female,25.84,0,no,northwest,28923.13692
25,male,26.22,0,no,northeast,2721.3208
62,female,26.29,0,yes,southeast,27808.7251
23,male,34.4,0,no,southwest,1826.843
56,female,39.82,0,no,southeast,11090.7178
27,male,42.13,0,yes,southeast,39611.7577
19,male,24.6,1,no,southwest,1837.237
52,female,30.78,1,no,northeast,10797.3362
23,male,23.845,0,no,northeast,2395.17155
56,male,40.3,0,no,southwest,10602.385
30,male,35.3,0,yes,southwest,36837.467
60,female,36.005,0,no,northeast,13228.84695
30,female,32.4,1,no,southwest,4149.736
18,male,34.1,0,no,southeast,1137.011
34,female,31.92,1,yes,northeast,37701.8768
37,male,28.025,2,no,northwest,6203.90175
59,female,27.72,3,no,southeast,14001.1338
63,female,23.085,0,no,northeast,14451.83515
55,female,32.775,2,no,northwest,12268.63225
23,male,17.385,1,no,northwest,2775.19215
31,male,36.3,2,yes,southwest,38711
22,male,35.6,0,yes,southwest,35585.576
18,female,26.315,0,no,northeast,2198.18985
19,female,28.6,5,no,southwest,4687.797
63,male,28.31,0,no,northwest,13770.0979
28,male,36.4,1,yes,southwest,51194.55914
19,male,20.425,0,no,northwest,1625.43375
62,female,32.965,3,no,northwest,15612.19335
26,male,20.8,0,no,southwest,2302.3
35,male,36.67,1,yes,northeast,39774.2763
60,male,39.9,0,yes,southwest,48173.361
24,female,26.6,0,no,northeast,3046.062
31,female,36.63,2,no,southeast,4949.7587
41,male,21.78,1,no,southeast,6272.4772
37,female,30.8,2,no,southeast,6313.759
38,male,37.05,1,no,northeast,6079.6715
55,male,37.3,0,no,southwest,20630.28351
18,female,38.665,2,no,northeast,3393.35635
28,female,34.77,0,no,northwest,3556.9223
60,female,24.53,0,no,southeast,12629.8967
36,male,35.2,1,yes,southeast,38709.176
18,female,35.625,0,no,northeast,2211.13075
21,female,33.63,2,no,northwest,3579.8287
48,male,28,1,yes,southwest,23568.272
36,male,34.43,0,yes,southeast,37742.5757
40,female,28.69,3,no,northwest,8059.6791
58,male,36.955,2,yes,northwest,47496.49445
58,female,31.825,2,no,northeast,13607.36875
18,male,31.68,2,yes,southeast,34303.1672
53,female,22.88,1,yes,southeast,23244.7902
34,female,37.335,2,no,northwest,5989.52365
43,male,27.36,3,no,northeast,8606.2174
25,male,33.66,4,no,southeast,4504.6624
64,male,24.7,1,no,northwest,30166.61817
28,female,25.935,1,no,northwest,4133.64165
20,female,22.42,0,yes,northwest,14711.7438
19,female,28.9,0,no,southwest,1743.214
61,female,39.1,2,no,southwest,14235.072
40,male,26.315,1,no,northwest,6389.37785
40,female,36.19,0,no,southeast,5920.1041
28,male,23.98,3,yes,southeast,17663.1442
27,female,24.75,0,yes,southeast,16577.7795
31,male,28.5,5,no,northeast,6799.458
53,female,28.1,3,no,southwest,11741.726
58,male,32.01,1,no,southeast,11946.6259
44,male,27.4,2,no,southwest,7726.854
57,male,34.01,0,no,northwest,11356.6609
29,female,29.59,1,no,southeast,3947.4131
21,male,35.53,0,no,southeast,1532.4697
22,female,39.805,0,no,northeast,2755.02095
41,female,32.965,0,no,northwest,6571.02435
31,male,26.885,1,no,northeast,4441.21315
45,female,38.285,0,no,northeast,7935.29115
22,male,37.62,1,yes,southeast,37165.1638
48,female,41.23,4,no,northwest,11033.6617
37,female,34.8,2,yes,southwest,39836.519
45,male,22.895,2,yes,northwest,21098.55405
57,female,31.16,0,yes,northwest,43578.9394
56,female,27.2,0,no,southwest,11073.176
46,female,27.74,0,no,northwest,8026.6666
55,female,26.98,0,no,northwest,11082.5772
21,female,39.49,0,no,southeast,2026.9741
53,female,24.795,1,no,northwest,10942.13205
59,male,29.83,3,yes,northeast,30184.9367
35,male,34.77,2,no,northwest,5729.0053
64,female,31.3,2,yes,southwest,47291.055
28,female,37.62,1,no,southeast,3766.8838
54,female,30.8,3,no,southwest,12105.32
55,male,38.28,0,no,southeast,10226.2842
56,male,19.95,0,yes,northeast,22412.6485
38,male,19.3,0,yes,southwest,15820.699
41,female,31.6,0,no,southwest,6186.127
30,male,25.46,0,no,northeast,3645.0894
18,female,30.115,0,no,northeast,21344.8467
61,female,29.92,3,yes,southeast,30942.1918
34,female,27.5,1,no,southwest,5003.853
20,male,28.025,1,yes,northwest,17560.37975
19,female,28.4,1,no,southwest,2331.519
26,male,30.875,2,no,northwest,3877.30425
29,male,27.94,0,no,southeast,2867.1196
63,male,35.09,0,yes,southeast,47055.5321
54,male,33.63,1,no,northwest,10825.2537
55,female,29.7,2,no,southwest,11881.358
37,male,30.8,0,no,southwest,4646.759
21,female,35.72,0,no,northwest,2404.7338
52,male,32.205,3,no,northeast,11488.31695
60,male,28.595,0,no,northeast,30259.99556
58,male,49.06,0,no,southeast,11381.3254
29,female,27.94,1,yes,southeast,19107.7796
49,female,27.17,0,no,southeast,8601.3293
37,female,23.37,2,no,northwest,6686.4313
44,male,37.1,2,no,southwest,7740.337
18,male,23.75,0,no,northeast,1705.6245
20,female,28.975,0,no,northwest,2257.47525
44,male,31.35,1,yes,northeast,39556.4945
47,female,33.915,3,no,northwest,10115.00885
26,female,28.785,0,no,northeast,3385.39915
19,female,28.3,0,yes,southwest,17081.08
52,female,37.4,0,no,southwest,9634.538
32,female,17.765,2,yes,northwest,32734.1863
38,male,34.7,2,no,southwest,6082.405
59,female,26.505,0,no,northeast,12815.44495
61,female,22.04,0,no,northeast,13616.3586
53,female,35.9,2,no,southwest,11163.568
19,male,25.555,0,no,northwest,1632.56445
20,female,28.785,0,no,northeast,2457.21115
22,female,28.05,0,no,southeast,2155.6815
19,male,34.1,0,no,southwest,1261.442
22,male,25.175,0,no,northwest,2045.68525
54,female,31.9,3,no,southeast,27322.73386
22,female,36,0,no,southwest,2166.732
34,male,22.42,2,no,northeast,27375.90478
26,male,32.49,1,no,northeast,3490.5491
34,male,25.3,2,yes,southeast,18972.495
29,male,29.735,2,no,northwest,18157.876
30,male,28.69,3,yes,northwest,20745.9891
29,female,38.83,3,no,southeast,5138.2567
46,male,30.495,3,yes,northwest,40720.55105
51,female,37.73,1,no,southeast,9877.6077
53,female,37.43,1,no,northwest,10959.6947
19,male,28.4,1,no,southwest,1842.519
35,male,24.13,1,no,northwest,5125.2157
48,male,29.7,0,no,southeast,7789.635
32,female,37.145,3,no,northeast,6334.34355
42,female,23.37,0,yes,northeast,19964.7463
40,female,25.46,1,no,northeast,7077.1894
44,male,39.52,0,no,northwest,6948.7008
48,male,24.42,0,yes,southeast,21223.6758
18,male,25.175,0,yes,northeast,15518.18025
30,male,35.53,0,yes,southeast,36950.2567
50,female,27.83,3,no,southeast,19749.38338
42,female,26.6,0,yes,northwest,21348.706
18,female,36.85,0,yes,southeast,36149.4835
54,male,39.6,1,no,southwest,10450.552
32,female,29.8,2,no,southwest,5152.134
37,male,29.64,0,no,northwest,5028.1466
47,male,28.215,4,no,northeast,10407.08585
20,female,37,5,no,southwest,4830.63
32,female,33.155,3,no,northwest,6128.79745
19,female,31.825,1,no,northwest,2719.27975
27,male,18.905,3,no,northeast,4827.90495
63,male,41.47,0,no,southeast,13405.3903
49,male,30.3,0,no,southwest,8116.68
18,male,15.96,0,no,northeast,1694.7964
35,female,34.8,1,no,southwest,5246.047
24,female,33.345,0,no,northwest,2855.43755
63,female,37.7,0,yes,southwest,48824.45
38,male,27.835,2,no,northwest,6455.86265
54,male,29.2,1,no,southwest,10436.096
46,female,28.9,2,no,southwest,8823.279
41,female,33.155,3,no,northeast,8538.28845
58,male,28.595,0,no,northwest,11735.87905
18,female,38.28,0,no,southeast,1631.8212
22,male,19.95,3,no,northeast,4005.4225
44,female,26.41,0,no,northwest,7419.4779
44,male,30.69,2,no,southeast,7731.4271
36,male,41.895,3,yes,northeast,43753.33705
26,female,29.92,2,no,southeast,3981.9768
30,female,30.9,3,no,southwest,5325.651
41,female,32.2,1,no,southwest,6775.961
29,female,32.11,2,no,northwest,4922.9159
61,male,31.57,0,no,southeast,12557.6053
36,female,26.2,0,no,southwest,4883.866
25,male,25.74,0,no,southeast,2137.6536
56,female,26.6,1,no,northwest,12044.342
18,male,34.43,0,no,southeast,1137.4697
19,male,30.59,0,no,northwest,1639.5631
39,female,32.8,0,no,southwest,5649.715
45,female,28.6,2,no,southeast,8516.829
51,female,18.05,0,no,northwest,9644.2525
64,female,39.33,0,no,northeast,14901.5167
19,female,32.11,0,no,northwest,2130.6759
48,female,32.23,1,no,southeast,8871.1517
60,female,24.035,0,no,northwest,13012.20865
27,female,36.08,0,yes,southeast,37133.8982
46,male,22.3,0,no,southwest,7147.105
28,female,28.88,1,no,northeast,4337.7352
59,male,26.4,0,no,southeast,11743.299
35,male,27.74,2,yes,northeast,20984.0936
63,female,31.8,0,no,southwest,13880.949
40,male,41.23,1,no,northeast,6610.1097
20,male,33,1,no,southwest,1980.07
40,male,30.875,4,no,northwest,8162.71625
24,male,28.5,2,no,northwest,3537.703
34,female,26.73,1,no,southeast,5002.7827
45,female,30.9,2,no,southwest,8520.026
41,female,37.1,2,no,southwest,7371.772
53,female,26.6,0,no,northwest,10355.641
27,male,23.1,0,no,southeast,2483.736
26,female,29.92,1,no,southeast,3392.9768
24,female,23.21,0,no,southeast,25081.76784
34,female,33.7,1,no,southwest,5012.471
53,female,33.25,0,no,northeast,10564.8845
32,male,30.8,3,no,southwest,5253.524
19,male,34.8,0,yes,southwest,34779.615
42,male,24.64,0,yes,southeast,19515.5416
55,male,33.88,3,no,southeast,11987.1682
28,male,38.06,0,no,southeast,2689.4954
58,female,41.91,0,no,southeast,24227.33724
41,female,31.635,1,no,northeast,7358.17565
47,male,25.46,2,no,northeast,9225.2564
42,female,36.195,1,no,northwest,7443.64305
59,female,27.83,3,no,southeast,14001.2867
19,female,17.8,0,no,southwest,1727.785
59,male,27.5,1,no,southwest,12333.828
39,male,24.51,2,no,northwest,6710.1919
40,female,22.22,2,yes,southeast,19444.2658
18,female,26.73,0,no,southeast,1615.7667
31,male,38.39,2,no,southeast,4463.2051
19,male,29.07,0,yes,northwest,17352.6803
44,male,38.06,1,no,southeast,7152.6714
23,female,36.67,2,yes,northeast,38511.6283
33,female,22.135,1,no,northeast,5354.07465
55,female,26.8,1,no,southwest,35160.13457
40,male,35.3,3,no,southwest,7196.867
63,female,27.74,0,yes,northeast,29523.1656
54,male,30.02,0,no,northwest,24476.47851
60,female,38.06,0,no,southeast,12648.7034
24,male,35.86,0,no,southeast,1986.9334
19,male,20.9,1,no,southwest,1832.094
29,male,28.975,1,no,northeast,4040.55825
18,male,17.29,2,yes,northeast,12829.4551
63,female,32.2,2,yes,southwest,47305.305
54,male,34.21,2,yes,southeast,44260.7499
27,male,30.3,3,no,southwest,4260.744
50,male,31.825,0,yes,northeast,41097.16175
55,female,25.365,3,no,northeast,13047.33235
56,male,33.63,0,yes,northwest,43921.1837
38,female,40.15,0,no,southeast,5400.9805
51,male,24.415,4,no,northwest,11520.09985
19,male,31.92,0,yes,northwest,33750.2918
58,female,25.2,0,no,southwest,11837.16
20,female,26.84,1,yes,southeast,17085.2676
52,male,24.32,3,yes,northeast,24869.8368
19,male,36.955,0,yes,northwest,36219.40545
53,female,38.06,3,no,southeast,20462.99766
46,male,42.35,3,yes,southeast,46151.1245
40,male,19.8,1,yes,southeast,17179.522
59,female,32.395,3,no,northeast,14590.63205
45,male,30.2,1,no,southwest,7441.053
49,male,25.84,1,no,northeast,9282.4806
18,male,29.37,1,no,southeast,1719.4363
50,male,34.2,2,yes,southwest,42856.838
41,male,37.05,2,no,northwest,7265.7025
50,male,27.455,1,no,northeast,9617.66245
25,male,27.55,0,no,northwest,2523.1695
47,female,26.6,2,no,northeast,9715.841
19,male,20.615,2,no,northwest,2803.69785
22,female,24.3,0,no,southwest,2150.469
59,male,31.79,2,no,southeast,12928.7911
51,female,21.56,1,no,southeast,9855.1314
40,female,28.12,1,yes,northeast,22331.5668
54,male,40.565,3,yes,northeast,48549.17835
30,male,27.645,1,no,northeast,4237.12655
55,female,32.395,1,no,northeast,11879.10405
52,female,31.2,0,no,southwest,9625.92
46,male,26.62,1,no,southeast,7742.1098
46,female,48.07,2,no,northeast,9432.9253
63,female,26.22,0,no,northwest,14256.1928
59,female,36.765,1,yes,northeast,47896.79135
52,male,26.4,3,no,southeast,25992.82104
28,female,33.4,0,no,southwest,3172.018
29,male,29.64,1,no,northeast,20277.80751
25,male,45.54,2,yes,southeast,42112.2356
22,female,28.82,0,no,southeast,2156.7518
25,male,26.8,3,no,southwest,3906.127
18,male,22.99,0,no,northeast,1704.5681
19,male,27.7,0,yes,southwest,16297.846
47,male,25.41,1,yes,southeast,21978.6769
31,male,34.39,3,yes,northwest,38746.3551
48,female,28.88,1,no,northwest,9249.4952
36,male,27.55,3,no,northeast,6746.7425
53,female,22.61,3,yes,northeast,24873.3849
56,female,37.51,2,no,southeast,12265.5069
28,female,33,2,no,southeast,4349.462
57,female,38,2,no,southwest,12646.207
29,male,33.345,2,no,northwest,19442.3535
28,female,27.5,2,no,southwest,20177.67113
30,female,33.33,1,no,southeast,4151.0287
58,male,34.865,0,no,northeast,11944.59435
41,female,33.06,2,no,northwest,7749.1564
50,male,26.6,0,no,southwest,8444.474
19,female,24.7,0,no,southwest,1737.376
43,male,35.97,3,yes,southeast,42124.5153
49,male,35.86,0,no,southeast,8124.4084
27,female,31.4,0,yes,southwest,34838.873
52,male,33.25,0,no,northeast,9722.7695
50,male,32.205,0,no,northwest,8835.26495
54,male,32.775,0,no,northeast,10435.06525
44,female,27.645,0,no,northwest,7421.19455
32,male,37.335,1,no,northeast,4667.60765
34,male,25.27,1,no,northwest,4894.7533
26,female,29.64,4,no,northeast,24671.66334
34,male,30.8,0,yes,southwest,35491.64
57,male,40.945,0,no,northeast,11566.30055
29,male,27.2,0,no,southwest,2866.091
40,male,34.105,1,no,northeast,6600.20595
27,female,23.21,1,no,southeast,3561.8889
45,male,36.48,2,yes,northwest,42760.5022
64,female,33.8,1,yes,southwest,47928.03
52,male,36.7,0,no,southwest,9144.565
61,female,36.385,1,yes,northeast,48517.56315
52,male,27.36,0,yes,northwest,24393.6224
61,female,31.16,0,no,northwest,13429.0354
56,female,28.785,0,no,northeast,11658.37915
43,female,35.72,2,no,northeast,19144.57652
64,male,34.5,0,no,southwest,13822.803
60,male,25.74,0,no,southeast,12142.5786
62,male,27.55,1,no,northwest,13937.6665
50,male,32.3,1,yes,northeast,41919.097
46,female,27.72,1,no,southeast,8232.6388
24,female,27.6,0,no,southwest,18955.22017
62,male,30.02,0,no,northwest,13352.0998
60,female,27.55,0,no,northeast,13217.0945
63,male,36.765,0,no,northeast,13981.85035
49,female,41.47,4,no,southeast,10977.2063
34,female,29.26,3,no,southeast,6184.2994
33,male,35.75,2,no,southeast,4889.9995
46,male,33.345,1,no,northeast,8334.45755
36,female,29.92,1,no,southeast,5478.0368
19,male,27.835,0,no,northwest,1635.73365
57,female,23.18,0,no,northwest,11830.6072
50,female,25.6,0,no,southwest,8932.084
30,female,27.7,0,no,southwest,3554.203
33,male,35.245,0,no,northeast,12404.8791
18,female,38.28,0,no,southeast,14133.03775
46,male,27.6,0,no,southwest,24603.04837
46,male,43.89,3,no,southeast,8944.1151
47,male,29.83,3,no,northwest,9620.3307
23,male,41.91,0,no,southeast,1837.2819
18,female,20.79,0,no,southeast,1607.5101
48,female,32.3,2,no,northeast,10043.249
35,male,30.5,1,no,southwest,4751.07
19,female,21.7,0,yes,southwest,13844.506
21,female,26.4,1,no,southwest,2597.779
21,female,21.89,2,no,southeast,3180.5101
49,female,30.78,1,no,northeast,9778.3472
56,female,32.3,3,no,northeast,13430.265
42,female,24.985,2,no,northwest,8017.06115
44,male,32.015,2,no,northwest,8116.26885
18,male,30.4,3,no,northeast,3481.868
61,female,21.09,0,no,northwest,13415.0381
57,female,22.23,0,no,northeast,12029.2867
42,female,33.155,1,no,northeast,7639.41745
26,male,32.9,2,yes,southwest,36085.219
20,male,33.33,0,no,southeast,1391.5287
23,female,28.31,0,yes,northwest,18033.9679
39,female,24.89,3,yes,northeast,21659.9301
24,male,40.15,0,yes,southeast,38126.2465
64,female,30.115,3,no,northwest,16455.70785
62,male,31.46,1,no,southeast,27000.98473
27,female,17.955,2,yes,northeast,15006.57945
55,male,30.685,0,yes,northeast,42303.69215
55,male,33,0,no,southeast,20781.48892
35,female,43.34,2,no,southeast,5846.9176
44,male,22.135,2,no,northeast,8302.53565
19,male,34.4,0,no,southwest,1261.859
58,female,39.05,0,no,southeast,11856.4115
50,male,25.365,2,no,northwest,30284.64294
26,female,22.61,0,no,northwest,3176.8159
24,female,30.21,3,no,northwest,4618.0799
48,male,35.625,4,no,northeast,10736.87075
19,female,37.43,0,no,northwest,2138.0707
48,male,31.445,1,no,northeast,8964.06055
49,male,31.35,1,no,northeast,9290.1395
46,female,32.3,2,no,northeast,9411.005
46,male,19.855,0,no,northwest,7526.70645
43,female,34.4,3,no,southwest,8522.003
21,male,31.02,0,no,southeast,16586.49771
64,male,25.6,2,no,southwest,14988.432
18,female,38.17,0,no,southeast,1631.6683
51,female,20.6,0,no,southwest,9264.797
47,male,47.52,1,no,southeast,8083.9198
64,female,32.965,0,no,northwest,14692.66935
49,male,32.3,3,no,northwest,10269.46
31,male,20.4,0,no,southwest,3260.199
52,female,38.38,2,no,northeast,11396.9002
33,female,24.31,0,no,southeast,4185.0979
47,female,23.6,1,no,southwest,8539.671
38,male,21.12,3,no,southeast,6652.5288
32,male,30.03,1,no,southeast,4074.4537
19,male,17.48,0,no,northwest,1621.3402
44,female,20.235,1,yes,northeast,19594.80965
26,female,17.195,2,yes,northeast,14455.64405
25,male,23.9,5,no,southwest,5080.096
19,female,35.15,0,no,northwest,2134.9015
43,female,35.64,1,no,southeast,7345.7266
52,male,34.1,0,no,southeast,9140.951
36,female,22.6,2,yes,southwest,18608.262
64,male,39.16,1,no,southeast,14418.2804
63,female,26.98,0,yes,northwest,28950.4692
64,male,33.88,0,yes,southeast,46889.2612
61,male,35.86,0,yes,southeast,46599.1084
40,male,32.775,1,yes,northeast,39125.33225
25,male,30.59,0,no,northeast,2727.3951
48,male,30.2,2,no,southwest,8968.33
45,male,24.31,5,no,southeast,9788.8659
38,female,27.265,1,no,northeast,6555.07035
18,female,29.165,0,no,northeast,7323.734819
21,female,16.815,1,no,northeast,3167.45585
27,female,30.4,3,no,northwest,18804.7524
19,male,33.1,0,no,southwest,23082.95533
29,female,20.235,2,no,northwest,4906.40965
42,male,26.9,0,no,southwest,5969.723
60,female,30.5,0,no,southwest,12638.195
31,male,28.595,1,no,northwest,4243.59005
60,male,33.11,3,no,southeast,13919.8229
22,male,31.73,0,no,northeast,2254.7967
35,male,28.9,3,no,southwest,5926.846
52,female,46.75,5,no,southeast,12592.5345
26,male,29.45,0,no,northeast,2897.3235
31,female,32.68,1,no,northwest,4738.2682
33,female,33.5,0,yes,southwest,37079.372
18,male,43.01,0,no,southeast,1149.3959
59,female,36.52,1,no,southeast,28287.89766
56,male,26.695,1,yes,northwest,26109.32905
45,female,33.1,0,no,southwest,7345.084
60,male,29.64,0,no,northeast,12730.9996
56,female,25.65,0,no,northwest,11454.0215
40,female,29.6,0,no,southwest,5910.944
35,male,38.6,1,no,southwest,4762.329
39,male,29.6,4,no,southwest,7512.267
30,male,24.13,1,no,northwest,4032.2407
24,male,23.4,0,no,southwest,1969.614
20,male,29.735,0,no,northwest,1769.53165
32,male,46.53,2,no,southeast,4686.3887
59,male,37.4,0,no,southwest,21797.0004
55,female,30.14,2,no,southeast,11881.9696
57,female,30.495,0,no,northwest,11840.77505
56,male,39.6,0,no,southwest,10601.412
40,female,33,3,no,southeast,7682.67
49,female,36.63,3,no,southeast,10381.4787
42,male,30,0,yes,southwest,22144.032
62,female,38.095,2,no,northeast,15230.32405
56,male,25.935,0,no,northeast,11165.41765
19,male,25.175,0,no,northwest,1632.03625
30,female,28.38,1,yes,southeast,19521.9682
60,female,28.7,1,no,southwest,13224.693
56,female,33.82,2,no,northwest,12643.3778
28,female,24.32,1,no,northeast,23288.9284
18,female,24.09,1,no,southeast,2201.0971
27,male,32.67,0,no,southeast,2497.0383
18,female,30.115,0,no,northeast,2203.47185
19,female,29.8,0,no,southwest,1744.465
47,female,33.345,0,no,northeast,20878.78443
54,male,25.1,3,yes,southwest,25382.297
61,male,28.31,1,yes,northwest,28868.6639
24,male,28.5,0,yes,northeast,35147.52848
25,male,35.625,0,no,northwest,2534.39375
21,male,36.85,0,no,southeast,1534.3045
23,male,32.56,0,no,southeast,1824.2854
63,male,41.325,3,no,northwest,15555.18875
49,male,37.51,2,no,southeast,9304.7019
18,female,31.35,0,no,southeast,1622.1885
51,female,39.5,1,no,southwest,9880.068
48,male,34.3,3,no,southwest,9563.029
31,female,31.065,0,no,northeast,4347.02335
54,female,21.47,3,no,northwest,12475.3513
19,male,28.7,0,no,southwest,1253.936
44,female,38.06,0,yes,southeast,48885.13561
53,male,31.16,1,no,northwest,10461.9794
19,female,32.9,0,no,southwest,1748.774
61,female,25.08,0,no,southeast,24513.09126
18,female,25.08,0,no,northeast,2196.4732
61,male,43.4,0,no,southwest,12574.049
21,male,25.7,4,yes,southwest,17942.106
20,male,27.93,0,no,northeast,1967.0227
31,female,23.6,2,no,southwest,4931.647
45,male,28.7,2,no,southwest,8027.968
44,female,23.98,2,no,southeast,8211.1002
62,female,39.2,0,no,southwest,13470.86
29,male,34.4,0,yes,southwest,36197.699
43,male,26.03,0,no,northeast,6837.3687
51,male,23.21,1,yes,southeast,22218.1149
19,male,30.25,0,yes,southeast,32548.3405
38,female,28.93,1,no,southeast,5974.3847
37,male,30.875,3,no,northwest,6796.86325
22,male,31.35,1,no,northwest,2643.2685
21,male,23.75,2,no,northwest,3077.0955
24,female,25.27,0,no,northeast,3044.2133
57,female,28.7,0,no,southwest,11455.28
56,male,32.11,1,no,northeast,11763.0009
27,male,33.66,0,no,southeast,2498.4144
51,male,22.42,0,no,northeast,9361.3268
19,male,30.4,0,no,southwest,1256.299
39,male,28.3,1,yes,southwest,21082.16
58,male,35.7,0,no,southwest,11362.755
20,male,35.31,1,no,southeast,27724.28875
45,male,30.495,2,no,northwest,8413.46305
35,female,31,1,no,southwest,5240.765
31,male,30.875,0,no,northeast,3857.75925
50,female,27.36,0,no,northeast,25656.57526
32,female,44.22,0,no,southeast,3994.1778
51,female,33.915,0,no,northeast,9866.30485
38,female,37.73,0,no,southeast,5397.6167
42,male,26.07,1,yes,southeast,38245.59327
18,female,33.88,0,no,southeast,11482.63485
19,female,30.59,2,no,northwest,24059.68019
51,female,25.8,1,no,southwest,9861.025
46,male,39.425,1,no,northeast,8342.90875
18,male,25.46,0,no,northeast,1708.0014
57,male,42.13,1,yes,southeast,48675.5177
62,female,31.73,0,no,northeast,14043.4767
59,male,29.7,2,no,southeast,12925.886
37,male,36.19,0,no,southeast,19214.70553
64,male,40.48,0,no,southeast,13831.1152
38,male,28.025,1,no,northeast,6067.12675
33,female,38.9,3,no,southwest,5972.378
46,female,30.2,2,no,southwest,8825.086
46,female,28.05,1,no,southeast,8233.0975
53,male,31.35,0,no,southeast,27346.04207
34,female,38,3,no,southwest,6196.448
20,female,31.79,2,no,southeast,3056.3881
63,female,36.3,0,no,southeast,13887.204
54,female,47.41,0,yes,southeast,63770.42801
54,male,30.21,0,no,northwest,10231.4999
49,male,25.84,2,yes,northwest,23807.2406
28,male,35.435,0,no,northeast,3268.84665
54,female,46.7,2,no,southwest,11538.421
25,female,28.595,0,no,northeast,3213.62205
43,female,46.2,0,yes,southeast,45863.205
63,male,30.8,0,no,southwest,13390.559
32,female,28.93,0,no,southeast,3972.9247
62,male,21.4,0,no,southwest,12957.118
52,female,31.73,2,no,northwest,11187.6567
25,female,41.325,0,no,northeast,17878.90068
28,male,23.8,2,no,southwest,3847.674
46,male,33.44,1,no,northeast,8334.5896
34,male,34.21,0,no,southeast,3935.1799
35,female,34.105,3,yes,northwest,39983.42595
19,male,35.53,0,no,northwest,1646.4297
46,female,19.95,2,no,northwest,9193.8385
54,female,32.68,0,no,northeast,10923.9332
27,male,30.5,0,no,southwest,2494.022
50,male,44.77,1,no,southeast,9058.7303
18,female,32.12,2,no,southeast,2801.2588
19,female,30.495,0,no,northwest,2128.43105
38,female,40.565,1,no,northwest,6373.55735
41,male,30.59,2,no,northwest,7256.7231
49,female,31.9,5,no,southwest,11552.904
48,male,40.565,2,yes,northwest,45702.02235
31,female,29.1,0,no,southwest,3761.292
18,female,37.29,1,no,southeast,2219.4451
30,female,43.12,2,no,southeast,4753.6368
62,female,36.86,1,no,northeast,31620.00106
57,female,34.295,2,no,northeast,13224.05705
58,female,27.17,0,no,northwest,12222.8983
22,male,26.84,0,no,southeast,1664.9996
31,female,38.095,1,yes,northeast,58571.07448
52,male,30.2,1,no,southwest,9724.53
25,female,23.465,0,no,northeast,3206.49135
59,male,25.46,1,no,northeast,12913.9924
19,male,30.59,0,no,northwest,1639.5631
39,male,45.43,2,no,southeast,6356.2707
32,female,23.65,1,no,southeast,17626.23951
19,male,20.7,0,no,southwest,1242.816
33,female,28.27,1,no,southeast,4779.6023
21,male,20.235,3,no,northeast,3861.20965
34,female,30.21,1,yes,northwest,43943.8761
61,female,35.91,0,no,northeast,13635.6379
38,female,30.69,1,no,southeast,5976.8311
58,female,29,0,no,southwest,11842.442
47,male,19.57,1,no,northwest,8428.0693
20,male,31.13,2,no,southeast,2566.4707
21,female,21.85,1,yes,northeast,15359.1045
41,male,40.26,0,no,southeast,5709.1644
46,female,33.725,1,no,northeast,8823.98575
42,female,29.48,2,no,southeast,7640.3092
34,female,33.25,1,no,northeast,5594.8455
43,male,32.6,2,no,southwest,7441.501
52,female,37.525,2,no,northwest,33471.97189
18,female,39.16,0,no,southeast,1633.0444
51,male,31.635,0,no,northwest,9174.13565
56,female,25.3,0,no,southwest,11070.535
64,female,39.05,3,no,southeast,16085.1275
19,female,28.31,0,yes,northwest,17468.9839
51,female,34.1,0,no,southeast,9283.562
27,female,25.175,0,no,northeast,3558.62025
59,female,23.655,0,yes,northwest,25678.77845
28,male,26.98,2,no,northeast,4435.0942
30,male,37.8,2,yes,southwest,39241.442
47,female,29.37,1,no,southeast,8547.6913
38,female,34.8,2,no,southwest,6571.544
18,female,33.155,0,no,northeast,2207.69745
34,female,19,3,no,northeast,6753.038
20,female,33,0,no,southeast,1880.07
47,female,36.63,1,yes,southeast,42969.8527
56,female,28.595,0,no,northeast,11658.11505
49,male,25.6,2,yes,southwest,23306.547
19,female,33.11,0,yes,southeast,34439.8559
55,female,37.1,0,no,southwest,10713.644
30,male,31.4,1,no,southwest,3659.346
37,male,34.1,4,yes,southwest,40182.246
49,female,21.3,1,no,southwest,9182.17
18,male,33.535,0,yes,northeast,34617.84065
59,male,28.785,0,no,northwest,12129.61415
29,female,26.03,0,no,northwest,3736.4647
36,male,28.88,3,no,northeast,6748.5912
33,male,42.46,1,no,southeast,11326.71487
58,male,38,0,no,southwest,11365.952
44,female,38.95,0,yes,northwest,42983.4585
53,male,36.1,1,no,southwest,10085.846
24,male,29.3,0,no,southwest,1977.815
29,female,35.53,0,no,southeast,3366.6697
40,male,22.705,2,no,northeast,7173.35995
51,male,39.7,1,no,southwest,9391.346
64,male,38.19,0,no,northeast,14410.9321
19,female,24.51,1,no,northwest,2709.1119
35,female,38.095,2,no,northeast,24915.04626
39,male,26.41,0,yes,northeast,20149.3229
56,male,33.66,4,no,southeast,12949.1554
33,male,42.4,5,no,southwest,6666.243
42,male,28.31,3,yes,northwest,32787.45859
61,male,33.915,0,no,northeast,13143.86485
23,female,34.96,3,no,northwest,4466.6214
43,male,35.31,2,no,southeast,18806.14547
48,male,30.78,3,no,northeast,10141.1362
39,male,26.22,1,no,northwest,6123.5688
40,female,23.37,3,no,northeast,8252.2843
18,male,28.5,0,no,northeast,1712.227
58,female,32.965,0,no,northeast,12430.95335
49,female,42.68,2,no,southeast,9800.8882
53,female,39.6,1,no,southeast,10579.711
48,female,31.13,0,no,southeast,8280.6227
45,female,36.3,2,no,southeast,8527.532
59,female,35.2,0,no,southeast,12244.531
52,female,25.3,2,yes,southeast,24667.419
26,female,42.4,1,no,southwest,3410.324
27,male,33.155,2,no,northwest,4058.71245
48,female,35.91,1,no,northeast,26392.26029
57,female,28.785,4,no,northeast,14394.39815
37,male,46.53,3,no,southeast,6435.6237
57,female,23.98,1,no,southeast,22192.43711
32,female,31.54,1,no,northeast,5148.5526
18,male,33.66,0,no,southeast,1136.3994
64,female,22.99,0,yes,southeast,27037.9141
43,male,38.06,2,yes,southeast,42560.4304
49,male,28.7,1,no,southwest,8703.456
40,female,32.775,2,yes,northwest,40003.33225
62,male,32.015,0,yes,northeast,45710.20785
40,female,29.81,1,no,southeast,6500.2359
30,male,31.57,3,no,southeast,4837.5823
29,female,31.16,0,no,northeast,3943.5954
36,male,29.7,0,no,southeast,4399.731
41,female,31.02,0,no,southeast,6185.3208
44,female,43.89,2,yes,southeast,46200.9851
45,male,21.375,0,no,northwest,7222.78625
55,female,40.81,3,no,southeast,12485.8009
60,male,31.35,3,yes,northwest,46130.5265
56,male,36.1,3,no,southwest,12363.547
49,female,23.18,2,no,northwest,10156.7832
21,female,17.4,1,no,southwest,2585.269
19,male,20.3,0,no,southwest,1242.26
39,male,35.3,2,yes,southwest,40103.89
53,male,24.32,0,no,northwest,9863.4718
33,female,18.5,1,no,southwest,4766.022
53,male,26.41,2,no,northeast,11244.3769
42,male,26.125,2,no,northeast,7729.64575
40,male,41.69,0,no,southeast,5438.7491
47,female,24.1,1,no,southwest,26236.57997
27,male,31.13,1,yes,southeast,34806.4677
21,male,27.36,0,no,northeast,2104.1134
47,male,36.2,1,no,southwest,8068.185
20,male,32.395,1,no,northwest,2362.22905
24,male,23.655,0,no,northwest,2352.96845
27,female,34.8,1,no,southwest,3577.999
26,female,40.185,0,no,northwest,3201.24515
53,female,32.3,2,no,northeast,29186.48236
41,male,35.75,1,yes,southeast,40273.6455
56,male,33.725,0,no,northwest,10976.24575
23,female,39.27,2,no,southeast,3500.6123
21,female,34.87,0,no,southeast,2020.5523
50,female,44.745,0,no,northeast,9541.69555
53,male,41.47,0,no,southeast,9504.3103
34,female,26.41,1,no,northwest,5385.3379
47,female,29.545,1,no,northwest,8930.93455
33,female,32.9,2,no,southwest,5375.038
51,female,38.06,0,yes,southeast,44400.4064
49,male,28.69,3,no,northwest,10264.4421
31,female,30.495,3,no,northeast,6113.23105
36,female,27.74,0,no,northeast,5469.0066
18,male,35.2,1,no,southeast,1727.54
50,female,23.54,2,no,southeast,10107.2206
43,female,30.685,2,no,northwest,8310.83915
20,male,40.47,0,no,northeast,1984.4533
24,female,22.6,0,no,southwest,2457.502
60,male,28.9,0,no,southwest,12146.971
49,female,22.61,1,no,northwest,9566.9909
60,male,24.32,1,no,northwest,13112.6048
51,female,36.67,2,no,northwest,10848.1343
58,female,33.44,0,no,northwest,12231.6136
51,female,40.66,0,no,northeast,9875.6804
53,male,36.6,3,no,southwest,11264.541
62,male,37.4,0,no,southwest,12979.358
19,male,35.4,0,no,southwest,1263.249
50,female,27.075,1,no,northeast,10106.13425
30,female,39.05,3,yes,southeast,40932.4295
41,male,28.405,1,no,northwest,6664.68595
29,female,21.755,1,yes,northeast,16657.71745
18,female,40.28,0,no,northeast,2217.6012
41,female,36.08,1,no,southeast,6781.3542
35,male,24.42,3,yes,southeast,19361.9988
53,male,21.4,1,no,southwest,10065.413
24,female,30.1,3,no,southwest,4234.927
48,female,27.265,1,no,northeast,9447.25035
59,female,32.1,3,no,southwest,14007.222
49,female,34.77,1,no,northwest,9583.8933
37,female,38.39,0,yes,southeast,40419.0191
26,male,23.7,2,no,southwest,3484.331
23,male,31.73,3,yes,northeast,36189.1017
29,male,35.5,2,yes,southwest,44585.45587
45,male,24.035,2,no,northeast,8604.48365
27,male,29.15,0,yes,southeast,18246.4955
53,male,34.105,0,yes,northeast,43254.41795
31,female,26.62,0,no,southeast,3757.8448
50,male,26.41,0,no,northwest,8827.2099
50,female,30.115,1,no,northwest,9910.35985
34,male,27,2,no,southwest,11737.84884
19,male,21.755,0,no,northwest,1627.28245
47,female,36,1,no,southwest,8556.907
28,male,30.875,0,no,northwest,3062.50825
37,female,26.4,0,yes,southeast,19539.243
21,male,28.975,0,no,northwest,1906.35825
64,male,37.905,0,no,northwest,14210.53595
58,female,22.77,0,no,southeast,11833.7823
24,male,33.63,4,no,northeast,17128.42608
31,male,27.645,2,no,northeast,5031.26955
39,female,22.8,3,no,northeast,7985.815
47,female,27.83,0,yes,southeast,23065.4207
30,male,37.43,3,no,northeast,5428.7277
18,male,38.17,0,yes,southeast,36307.7983
22,female,34.58,2,no,northeast,3925.7582
23,male,35.2,1,no,southwest,2416.955
33,male,27.1,1,yes,southwest,19040.876
27,male,26.03,0,no,northeast,3070.8087
45,female,25.175,2,no,northeast,9095.06825
57,female,31.825,0,no,northwest,11842.62375
47,male,32.3,1,no,southwest,8062.764
42,female,29,1,no,southwest,7050.642
64,female,39.7,0,no,southwest,14319.031
38,female,19.475,2,no,northwest,6933.24225
61,male,36.1,3,no,southwest,27941.28758
53,female,26.7,2,no,southwest,11150.78
44,female,36.48,0,no,northeast,12797.20962
19,female,28.88,0,yes,northwest,17748.5062
41,male,34.2,2,no,northwest,7261.741
51,male,33.33,3,no,southeast,10560.4917
40,male,32.3,2,no,northwest,6986.697
45,male,39.805,0,no,northeast,7448.40395
35,male,34.32,3,no,southeast,5934.3798
53,male,28.88,0,no,northwest,9869.8102
30,male,24.4,3,yes,southwest,18259.216
18,male,41.14,0,no,southeast,1146.7966
51,male,35.97,1,no,southeast,9386.1613
50,female,27.6,1,yes,southwest,24520.264
31,female,29.26,1,no,southeast,4350.5144
35,female,27.7,3,no,southwest,6414.178
60,male,36.955,0,no,northeast,12741.16745
21,male,36.86,0,no,northwest,1917.3184
29,male,22.515,3,no,northeast,5209.57885
62,female,29.92,0,no,southeast,13457.9608
39,female,41.8,0,no,southeast,5662.225
19,male,27.6,0,no,southwest,1252.407
22,female,23.18,0,no,northeast,2731.9122
53,male,20.9,0,yes,southeast,21195.818
39,female,31.92,2,no,northwest,7209.4918
27,male,28.5,0,yes,northwest,18310.742
30,male,44.22,2,no,southeast,4266.1658
30,female,22.895,1,no,northeast,4719.52405
58,female,33.1,0,no,southwest,11848.141
33,male,24.795,0,yes,northeast,17904.52705
42,female,26.18,1,no,southeast,7046.7222
64,female,35.97,0,no,southeast,14313.8463
21,male,22.3,1,no,southwest,2103.08
18,female,42.24,0,yes,southeast,38792.6856
23,male,26.51,0,no,southeast,1815.8759
45,female,35.815,0,no,northwest,7731.85785
40,female,41.42,1,no,northwest,28476.73499
19,female,36.575,0,no,northwest,2136.88225
18,male,30.14,0,no,southeast,1131.5066
25,male,25.84,1,no,northeast,3309.7926
46,female,30.8,3,no,southwest,9414.92
33,female,42.94,3,no,northwest,6360.9936
54,male,21.01,2,no,southeast,11013.7119
28,male,22.515,2,no,northeast,4428.88785
36,male,34.43,2,no,southeast,5584.3057
20,female,31.46,0,no,southeast,1877.9294
24,female,24.225,0,no,northwest,2842.76075
23,male,37.1,3,no,southwest,3597.596
47,female,26.125,1,yes,northeast,23401.30575
33,female,35.53,0,yes,northwest,55135.40209
45,male,33.7,1,no,southwest,7445.918
26,male,17.67,0,no,northwest,2680.9493
18,female,31.13,0,no,southeast,1621.8827
44,female,29.81,2,no,southeast,8219.2039
60,male,24.32,0,no,northwest,12523.6048
64,female,31.825,2,no,northeast,16069.08475
56,male,31.79,2,yes,southeast,43813.8661
36,male,28.025,1,yes,northeast,20773.62775
41,male,30.78,3,yes,northeast,39597.4072
39,male,21.85,1,no,northwest,6117.4945
63,male,33.1,0,no,southwest,13393.756
36,female,25.84,0,no,northwest,5266.3656
28,female,23.845,2,no,northwest,4719.73655
58,male,34.39,0,no,northwest,11743.9341
36,male,33.82,1,no,northwest,5377.4578
42,male,35.97,2,no,southeast,7160.3303
36,male,31.5,0,no,southwest,4402.233
56,female,28.31,0,no,northeast,11657.7189
35,female,23.465,2,no,northeast,6402.29135
59,female,31.35,0,no,northwest,12622.1795
21,male,31.1,0,no,southwest,1526.312
59,male,24.7,0,no,northeast,12323.936
23,female,32.78,2,yes,southeast,36021.0112
57,female,29.81,0,yes,southeast,27533.9129
53,male,30.495,0,no,northeast,10072.05505
60,female,32.45,0,yes,southeast,45008.9555
51,female,34.2,1,no,southwest,9872.701
23,male,50.38,1,no,southeast,2438.0552
27,female,24.1,0,no,southwest,2974.126
55,male,32.775,0,no,northwest,10601.63225
37,female,30.78,0,yes,northeast,37270.1512
61,male,32.3,2,no,northwest,14119.62
46,female,35.53,0,yes,northeast,42111.6647
53,female,23.75,2,no,northeast,11729.6795
49,female,23.845,3,yes,northeast,24106.91255
20,female,29.6,0,no,southwest,1875.344
48,female,33.11,0,yes,southeast,40974.1649
25,male,24.13,0,yes,northwest,15817.9857
25,female,32.23,1,no,southeast,18218.16139
57,male,28.1,0,no,southwest,10965.446
37,female,47.6,2,yes,southwest,46113.511
38,female,28,3,no,southwest,7151.092
55,female,33.535,2,no,northwest,12269.68865
36,female,19.855,0,no,northeast,5458.04645
51,male,25.4,0,no,southwest,8782.469
40,male,29.9,2,no,southwest,6600.361
18,male,37.29,0,no,southeast,1141.4451
57,male,43.7,1,no,southwest,11576.13
61,male,23.655,0,no,northeast,13129.60345
25,female,24.3,3,no,southwest,4391.652
50,male,36.2,0,no,southwest,8457.818
26,female,29.48,1,no,southeast,3392.3652
42,male,24.86,0,no,southeast,5966.8874
43,male,30.1,1,no,southwest,6849.026
44,male,21.85,3,no,northeast,8891.1395
23,female,28.12,0,no,northwest,2690.1138
49,female,27.1,1,no,southwest,26140.3603
33,male,33.44,5,no,southeast,6653.7886
41,male,28.8,1,no,southwest,6282.235
37,female,29.5,2,no,southwest,6311.952
22,male,34.8,3,no,southwest,3443.064
23,male,27.36,1,no,northwest,2789.0574
21,female,22.135,0,no,northeast,2585.85065
51,female,37.05,3,yes,northeast,46255.1125
25,male,26.695,4,no,northwest,4877.98105
32,male,28.93,1,yes,southeast,19719.6947
57,male,28.975,0,yes,northeast,27218.43725
36,female,30.02,0,no,northwest,5272.1758
22,male,39.5,0,no,southwest,1682.597
57,male,33.63,1,no,northwest,11945.1327
64,female,26.885,0,yes,northwest,29330.98315
36,female,29.04,4,no,southeast,7243.8136
54,male,24.035,0,no,northeast,10422.91665
47,male,38.94,2,yes,southeast,44202.6536
62,male,32.11,0,no,northeast,13555.0049
61,female,44,0,no,southwest,13063.883
43,female,20.045,2,yes,northeast,19798.05455
19,male,25.555,1,no,northwest,2221.56445
18,female,40.26,0,no,southeast,1634.5734
19,female,22.515,0,no,northwest,2117.33885
49,male,22.515,0,no,northeast,8688.85885
60,male,40.92,0,yes,southeast,48673.5588
26,male,27.265,3,no,northeast,4661.28635
49,male,36.85,0,no,southeast,8125.7845
60,female,35.1,0,no,southwest,12644.589
26,female,29.355,2,no,northeast,4564.19145
27,male,32.585,3,no,northeast,4846.92015
44,female,32.34,1,no,southeast,7633.7206
63,male,39.8,3,no,southwest,15170.069
32,female,24.6,0,yes,southwest,17496.306
22,male,28.31,1,no,northwest,2639.0429
18,male,31.73,0,yes,northeast,33732.6867
59,female,26.695,3,no,northwest,14382.70905
44,female,27.5,1,no,southwest,7626.993
33,male,24.605,2,no,northwest,5257.50795
24,female,33.99,0,no,southeast,2473.3341
43,female,26.885,0,yes,northwest,21774.32215
45,male,22.895,0,yes,northeast,35069.37452
61,female,28.2,0,no,southwest,13041.921
35,female,34.21,1,no,southeast,5245.2269
62,female,25,0,no,southwest,13451.122
62,female,33.2,0,no,southwest,13462.52
38,male,31,1,no,southwest,5488.262
34,male,35.815,0,no,northwest,4320.41085
43,male,23.2,0,no,southwest,6250.435
50,male,32.11,2,no,northeast,25333.33284
19,female,23.4,2,no,southwest,2913.569
57,female,20.1,1,no,southwest,12032.326
62,female,39.16,0,no,southeast,13470.8044
41,male,34.21,1,no,southeast,6289.7549
26,male,46.53,1,no,southeast,2927.0647
39,female,32.5,1,no,southwest,6238.298
46,male,25.8,5,no,southwest,10096.97
45,female,35.3,0,no,southwest,7348.142
32,male,37.18,2,no,southeast,4673.3922
59,female,27.5,0,no,southwest,12233.828
44,male,29.735,2,no,northeast,32108.66282
39,female,24.225,5,no,northwest,8965.79575
18,male,26.18,2,no,southeast,2304.0022
53,male,29.48,0,no,southeast,9487.6442
18,male,23.21,0,no,southeast,1121.8739
50,female,46.09,1,no,southeast,9549.5651
18,female,40.185,0,no,northeast,2217.46915
19,male,22.61,0,no,northwest,1628.4709
62,male,39.93,0,no,southeast,12982.8747
56,female,35.8,1,no,southwest,11674.13
42,male,35.8,2,no,southwest,7160.094
37,male,34.2,1,yes,northeast,39047.285
42,male,31.255,0,no,northwest,6358.77645
25,male,29.7,3,yes,southwest,19933.458
57,male,18.335,0,no,northeast,11534.87265
51,male,42.9,2,yes,southeast,47462.894
30,female,28.405,1,no,northwest,4527.18295
44,male,30.2,2,yes,southwest,38998.546
34,male,27.835,1,yes,northwest,20009.63365
31,male,39.49,1,no,southeast,3875.7341
54,male,30.8,1,yes,southeast,41999.52
24,male,26.79,1,no,northwest,12609.88702
43,male,34.96,1,yes,northeast,41034.2214
48,male,36.67,1,no,northwest,28468.91901
19,female,39.615,1,no,northwest,2730.10785
29,female,25.9,0,no,southwest,3353.284
63,female,35.2,1,no,southeast,14474.675
46,male,24.795,3,no,northeast,9500.57305
52,male,36.765,2,no,northwest,26467.09737
35,male,27.1,1,no,southwest,4746.344
51,male,24.795,2,yes,northwest,23967.38305
44,male,25.365,1,no,northwest,7518.02535
21,male,25.745,2,no,northeast,3279.86855
39,female,34.32,5,no,southeast,8596.8278
50,female,28.16,3,no,southeast,10702.6424
34,female,23.56,0,no,northeast,4992.3764
22,female,20.235,0,no,northwest,2527.81865
19,female,40.5,0,no,southwest,1759.338
26,male,35.42,0,no,southeast,2322.6218
29,male,22.895,0,yes,northeast,16138.76205
48,male,40.15,0,no,southeast,7804.1605
26,male,29.15,1,no,southeast,2902.9065
45,female,39.995,3,no,northeast,9704.66805
36,female,29.92,0,no,southeast,4889.0368
54,male,25.46,1,no,northeast,25517.11363
34,male,21.375,0,no,northeast,4500.33925
31,male,25.9,3,yes,southwest,19199.944
27,female,30.59,1,no,northeast,16796.41194
20,male,30.115,5,no,northeast,4915.05985
44,female,25.8,1,no,southwest,7624.63
43,male,30.115,3,no,northwest,8410.04685
45,female,27.645,1,no,northwest,28340.18885
34,male,34.675,0,no,northeast,4518.82625
24,female,20.52,0,yes,northeast,14571.8908
26,female,19.8,1,no,southwest,3378.91
38,female,27.835,2,no,northeast,7144.86265
50,female,31.6,2,no,southwest,10118.424
38,male,28.27,1,no,southeast,5484.4673
27,female,20.045,3,yes,northwest,16420.49455
39,female,23.275,3,no,northeast,7986.47525
39,female,34.1,3,no,southwest,7418.522
63,female,36.85,0,no,southeast,13887.9685
33,female,36.29,3,no,northeast,6551.7501
36,female,26.885,0,no,northwest,5267.81815
30,male,22.99,2,yes,northwest,17361.7661
24,male,32.7,0,yes,southwest,34472.841
24,male,25.8,0,no,southwest,1972.95
48,male,29.6,0,no,southwest,21232.18226
47,male,19.19,1,no,northeast,8627.5411
29,male,31.73,2,no,northwest,4433.3877
28,male,29.26,2,no,northeast,4438.2634
47,male,28.215,3,yes,northwest,24915.22085
25,male,24.985,2,no,northeast,23241.47453
51,male,27.74,1,no,northeast,9957.7216
48,female,22.8,0,no,southwest,8269.044
43,male,20.13,2,yes,southeast,18767.7377
61,female,33.33,4,no,southeast,36580.28216
48,male,32.3,1,no,northwest,8765.249
38,female,27.6,0,no,southwest,5383.536
59,male,25.46,0,no,northwest,12124.9924
19,female,24.605,1,no,northwest,2709.24395
26,female,34.2,2,no,southwest,3987.926
54,female,35.815,3,no,northwest,12495.29085
21,female,32.68,2,no,northwest,26018.95052
51,male,37,0,no,southwest,8798.593
22,female,31.02,3,yes,southeast,35595.5898
47,male,36.08,1,yes,southeast,42211.1382
18,male,23.32,1,no,southeast,1711.0268
47,female,45.32,1,no,southeast,8569.8618
21,female,34.6,0,no,southwest,2020.177
19,male,26.03,1,yes,northwest,16450.8947
23,male,18.715,0,no,northwest,21595.38229
54,male,31.6,0,no,southwest,9850.432
37,female,17.29,2,no,northeast,6877.9801
46,female,23.655,1,yes,northwest,21677.28345
55,female,35.2,0,yes,southeast,44423.803
30,female,27.93,0,no,northeast,4137.5227
18,male,21.565,0,yes,northeast,13747.87235
61,male,38.38,0,no,northwest,12950.0712
54,female,23,3,no,southwest,12094.478
22,male,37.07,2,yes,southeast,37484.4493
45,female,30.495,1,yes,northwest,39725.51805
22,male,28.88,0,no,northeast,2250.8352
19,male,27.265,2,no,northwest,22493.65964
35,female,28.025,0,yes,northwest,20234.85475
18,male,23.085,0,no,northeast,1704.70015
20,male,30.685,0,yes,northeast,33475.81715
28,female,25.8,0,no,southwest,3161.454
55,male,35.245,1,no,northeast,11394.06555
43,female,24.7,2,yes,northwest,21880.82
43,female,25.08,0,no,northeast,7325.0482
22,male,52.58,1,yes,southeast,44501.3982
25,female,22.515,1,no,northwest,3594.17085
49,male,30.9,0,yes,southwest,39727.614
44,female,36.955,1,no,northwest,8023.13545
64,male,26.41,0,no,northeast,14394.5579
49,male,29.83,1,no,northeast,9288.0267
47,male,29.8,3,yes,southwest,25309.489
27,female,21.47,0,no,northwest,3353.4703
55,male,27.645,0,no,northwest,10594.50155
48,female,28.9,0,no,southwest,8277.523
45,female,31.79,0,no,southeast,17929.30337
24,female,39.49,0,no,southeast,2480.9791
32,male,33.82,1,no,northwest,4462.7218
24,male,32.01,0,no,southeast,1981.5819
57,male,27.94,1,no,southeast,11554.2236
59,male,41.14,1,yes,southeast,48970.2476
36,male,28.595,3,no,northwest,6548.19505
29,female,25.6,4,no,southwest,5708.867
42,female,25.3,1,no,southwest,7045.499
48,male,37.29,2,no,southeast,8978.1851
39,male,42.655,0,no,northeast,5757.41345
63,male,21.66,1,no,northwest,14349.8544
54,female,31.9,1,no,southeast,10928.849
37,male,37.07,1,yes,southeast,39871.7043
63,male,31.445,0,no,northeast,13974.45555
21,male,31.255,0,no,northwest,1909.52745
54,female,28.88,2,no,northeast,12096.6512
60,female,18.335,0,no,northeast,13204.28565
32,female,29.59,1,no,southeast,4562.8421
47,female,32,1,no,southwest,8551.347
21,male,26.03,0,no,northeast,2102.2647
28,male,31.68,0,yes,southeast,34672.1472
63,male,33.66,3,no,southeast,15161.5344
18,male,21.78,2,no,southeast,11884.04858
32,male,27.835,1,no,northwest,4454.40265
38,male,19.95,1,no,northwest,5855.9025
32,male,31.5,1,no,southwest,4076.497
62,female,30.495,2,no,northwest,15019.76005
39,female,18.3,5,yes,southwest,19023.26
55,male,28.975,0,no,northeast,10796.35025
57,male,31.54,0,no,northwest,11353.2276
52,male,47.74,1,no,southeast,9748.9106
56,male,22.1,0,no,southwest,10577.087
47,male,36.19,0,yes,southeast,41676.0811
55,female,29.83,0,no,northeast,11286.5387
23,male,32.7,3,no,southwest,3591.48
22,female,30.4,0,yes,northwest,33907.548
50,female,33.7,4,no,southwest,11299.343
18,female,31.35,4,no,northeast,4561.1885
51,female,34.96,2,yes,northeast,44641.1974
22,male,33.77,0,no,southeast,1674.6323
52,female,30.875,0,no,northeast,23045.56616
25,female,33.99,1,no,southeast,3227.1211
33,female,19.095,2,yes,northeast,16776.30405
53,male,28.6,3,no,southwest,11253.421
29,male,38.94,1,no,southeast,3471.4096
58,male,36.08,0,no,southeast,11363.2832
37,male,29.8,0,no,southwest,20420.60465
54,female,31.24,0,no,southeast,10338.9316
49,female,29.925,0,no,northwest,8988.15875
50,female,26.22,2,no,northwest,10493.9458
26,male,30,1,no,southwest,2904.088
45,male,20.35,3,no,southeast,8605.3615
54,female,32.3,1,no,northeast,11512.405
38,male,38.39,3,yes,southeast,41949.2441
48,female,25.85,3,yes,southeast,24180.9335
28,female,26.315,3,no,northwest,5312.16985
23,male,24.51,0,no,northeast,2396.0959
55,male,32.67,1,no,southeast,10807.4863
41,male,29.64,5,no,northeast,9222.4026
25,male,33.33,2,yes,southeast,36124.5737
33,male,35.75,1,yes,southeast,38282.7495
30,female,19.95,3,no,northwest,5693.4305
23,female,31.4,0,yes,southwest,34166.273
46,male,38.17,2,no,southeast,8347.1643
53,female,36.86,3,yes,northwest,46661.4424
27,female,32.395,1,no,northeast,18903.49141
23,female,42.75,1,yes,northeast,40904.1995
63,female,25.08,0,no,northwest,14254.6082
55,male,29.9,0,no,southwest,10214.636
35,female,35.86,2,no,southeast,5836.5204
34,male,32.8,1,no,southwest,14358.36437
19,female,18.6,0,no,southwest,1728.897
39,female,23.87,5,no,southeast,8582.3023
27,male,45.9,2,no,southwest,3693.428
57,male,40.28,0,no,northeast,20709.02034
52,female,18.335,0,no,northwest,9991.03765
28,male,33.82,0,no,northwest,19673.33573
50,female,28.12,3,no,northwest,11085.5868
44,female,25,1,no,southwest,7623.518
26,female,22.23,0,no,northwest,3176.2877
33,male,30.25,0,no,southeast,3704.3545
19,female,32.49,0,yes,northwest,36898.73308
50,male,37.07,1,no,southeast,9048.0273
41,female,32.6,3,no,southwest,7954.517
52,female,24.86,0,no,southeast,27117.99378
39,male,32.34,2,no,southeast,6338.0756
50,male,32.3,2,no,southwest,9630.397
52,male,32.775,3,no,northwest,11289.10925
60,male,32.8,0,yes,southwest,52590.82939
20,female,31.92,0,no,northwest,2261.5688
55,male,21.5,1,no,southwest,10791.96
42,male,34.1,0,no,southwest,5979.731
18,female,30.305,0,no,northeast,2203.73595
58,female,36.48,0,no,northwest,12235.8392
43,female,32.56,3,yes,southeast,40941.2854
35,female,35.815,1,no,northwest,5630.45785
48,female,27.93,4,no,northwest,11015.1747
36,female,22.135,3,no,northeast,7228.21565
19,male,44.88,0,yes,southeast,39722.7462
23,female,23.18,2,no,northwest,14426.07385
20,female,30.59,0,no,northeast,2459.7201
32,female,41.1,0,no,southwest,3989.841
43,female,34.58,1,no,northwest,7727.2532
34,male,42.13,2,no,southeast,5124.1887
30,male,38.83,1,no,southeast,18963.17192
18,female,28.215,0,no,northeast,2200.83085
41,female,28.31,1,no,northwest,7153.5539
35,female,26.125,0,no,northeast,5227.98875
57,male,40.37,0,no,southeast,10982.5013
29,female,24.6,2,no,southwest,4529.477
32,male,35.2,2,no,southwest,4670.64
37,female,34.105,1,no,northwest,6112.35295
18,male,27.36,1,yes,northeast,17178.6824
43,female,26.7,2,yes,southwest,22478.6
56,female,41.91,0,no,southeast,11093.6229
38,male,29.26,2,no,northwest,6457.8434
29,male,32.11,2,no,northwest,4433.9159
22,female,27.1,0,no,southwest,2154.361
52,female,24.13,1,yes,northwest,23887.6627
40,female,27.4,1,no,southwest,6496.886
23,female,34.865,0,no,northeast,2899.48935
31,male,29.81,0,yes,southeast,19350.3689
42,female,41.325,1,no,northeast,7650.77375
24,female,29.925,0,no,northwest,2850.68375
25,female,30.3,0,no,southwest,2632.992
48,female,27.36,1,no,northeast,9447.3824
23,female,28.49,1,yes,southeast,18328.2381
45,male,23.56,2,no,northeast,8603.8234
20,male,35.625,3,yes,northwest,37465.34375
62,female,32.68,0,no,northwest,13844.7972
43,female,25.27,1,yes,northeast,21771.3423
23,female,28,0,no,southwest,13126.67745
31,female,32.775,2,no,northwest,5327.40025
41,female,21.755,1,no,northeast,13725.47184
58,female,32.395,1,no,northeast,13019.16105
48,female,36.575,0,no,northwest,8671.19125
31,female,21.755,0,no,northwest,4134.08245
19,female,27.93,3,no,northwest,18838.70366
19,female,30.02,0,yes,northwest,33307.5508
41,male,33.55,0,no,southeast,5699.8375
40,male,29.355,1,no,northwest,6393.60345
31,female,25.8,2,no,southwest,4934.705
37,male,24.32,2,no,northwest,6198.7518
46,male,40.375,2,no,northwest,8733.22925
22,male,32.11,0,no,northwest,2055.3249
51,male,32.3,1,no,northeast,9964.06
18,female,27.28,3,yes,southeast,18223.4512
35,male,17.86,1,no,northwest,5116.5004
59,female,34.8,2,no,southwest,36910.60803
36,male,33.4,2,yes,southwest,38415.474
37,female,25.555,1,yes,northeast,20296.86345
59,male,37.1,1,no,southwest,12347.172
36,male,30.875,1,no,northwest,5373.36425
39,male,34.1,2,no,southeast,23563.01618
18,male,21.47,0,no,northeast,1702.4553
52,female,33.3,2,no,southwest,10806.839
27,female,31.255,1,no,northwest,3956.07145
18,male,39.14,0,no,northeast,12890.05765
40,male,25.08,0,no,southeast,5415.6612
29,male,37.29,2,no,southeast,4058.1161
46,female,34.6,1,yes,southwest,41661.602
38,female,30.21,3,no,northwest,7537.1639
30,female,21.945,1,no,northeast,4718.20355
40,male,24.97,2,no,southeast,6593.5083
50,male,25.3,0,no,southeast,8442.667
20,female,24.42,0,yes,southeast,26125.67477
41,male,23.94,1,no,northeast,6858.4796
33,female,39.82,1,no,southeast,4795.6568
38,male,16.815,2,no,northeast,6640.54485
42,male,37.18,2,no,southeast,7162.0122
56,male,34.43,0,no,southeast,10594.2257
58,male,30.305,0,no,northeast,11938.25595
52,male,34.485,3,yes,northwest,60021.39897
20,female,21.8,0,yes,southwest,20167.33603
54,female,24.605,3,no,northwest,12479.70895
58,male,23.3,0,no,southwest,11345.519
45,female,27.83,2,no,southeast,8515.7587
26,male,31.065,0,no,northwest,2699.56835
63,female,21.66,0,no,northeast,14449.8544
58,female,28.215,0,no,northwest,12224.35085
37,male,22.705,3,no,northeast,6985.50695
25,female,42.13,1,no,southeast,3238.4357
52,male,41.8,2,yes,southeast,47269.854
64,male,36.96,2,yes,southeast,49577.6624
22,female,21.28,3,no,northwest,4296.2712
28,female,33.11,0,no,southeast,3171.6149
18,male,33.33,0,no,southeast,1135.9407
28,male,24.3,5,no,southwest,5615.369
45,female,25.7,3,no,southwest,9101.798
33,male,29.4,4,no,southwest,6059.173
18,female,39.82,0,no,southeast,1633.9618
32,male,33.63,1,yes,northeast,37607.5277
24,male,29.83,0,yes,northeast,18648.4217
19,male,19.8,0,no,southwest,1241.565
20,male,27.3,0,yes,southwest,16232.847
40,female,29.3,4,no,southwest,15828.82173
34,female,27.72,0,no,southeast,4415.1588
42,female,37.9,0,no,southwest,6474.013
51,female,36.385,3,no,northwest,11436.73815
54,female,27.645,1,no,northwest,11305.93455
55,male,37.715,3,no,northwest,30063.58055
52,female,23.18,0,no,northeast,10197.7722
32,female,20.52,0,no,northeast,4544.2348
28,male,37.1,1,no,southwest,3277.161
41,female,28.05,1,no,southeast,6770.1925
43,female,29.9,1,no,southwest,7337.748
49,female,33.345,2,no,northeast,10370.91255
64,male,23.76,0,yes,southeast,26926.5144
55,female,30.5,0,no,southwest,10704.47
24,male,31.065,0,yes,northeast,34254.05335
20,female,33.3,0,no,southwest,1880.487
45,male,27.5,3,no,southwest,8615.3
26,male,33.915,1,no,northwest,3292.52985
25,female,34.485,0,no,northwest,3021.80915
43,male,25.52,5,no,southeast,14478.33015
35,male,27.61,1,no,southeast,4747.0529
26,male,27.06,0,yes,southeast,17043.3414
57,male,23.7,0,no,southwest,10959.33
22,female,30.4,0,no,northeast,2741.948
32,female,29.735,0,no,northwest,4357.04365
39,male,29.925,1,yes,northeast,22462.04375
25,female,26.79,2,no,northwest,4189.1131
48,female,33.33,0,no,southeast,8283.6807
47,female,27.645,2,yes,northwest,24535.69855
18,female,21.66,0,yes,northeast,14283.4594
18,male,30.03,1,no,southeast,1720.3537
61,male,36.3,1,yes,southwest,47403.88
47,female,24.32,0,no,northeast,8534.6718
28,female,17.29,0,no,northeast,3732.6251
36,female,25.9,1,no,southwest,5472.449
20,male,39.4,2,yes,southwest,38344.566
44,male,34.32,1,no,southeast,7147.4728
38,female,19.95,2,no,northeast,7133.9025
19,male,34.9,0,yes,southwest,34828.654
21,male,23.21,0,no,southeast,1515.3449
46,male,25.745,3,no,northwest,9301.89355
58,male,25.175,0,no,northeast,11931.12525
20,male,22,1,no,southwest,1964.78
18,male,26.125,0,no,northeast,1708.92575
28,female,26.51,2,no,southeast,4340.4409
33,male,27.455,2,no,northwest,5261.46945
19,female,25.745,1,no,northwest,2710.82855
45,male,30.36,0,yes,southeast,62592.87309
62,male,30.875,3,yes,northwest,46718.16325
25,female,20.8,1,no,southwest,3208.787
43,male,27.8,0,yes,southwest,37829.7242
42,male,24.605,2,yes,northeast,21259.37795
24,female,27.72,0,no,southeast,2464.6188
29,female,21.85,0,yes,northeast,16115.3045
32,male,28.12,4,yes,northwest,21472.4788
25,female,30.2,0,yes,southwest,33900.653
41,male,32.2,2,no,southwest,6875.961
42,male,26.315,1,no,northwest,6940.90985
33,female,26.695,0,no,northwest,4571.41305
34,male,42.9,1,no,southwest,4536.259
19,female,34.7,2,yes,southwest,36397.576
30,female,23.655,3,yes,northwest,18765.87545
18,male,28.31,1,no,northeast,11272.33139
19,female,20.6,0,no,southwest,1731.677
18,male,53.13,0,no,southeast,1163.4627
35,male,39.71,4,no,northeast,19496.71917
39,female,26.315,2,no,northwest,7201.70085
31,male,31.065,3,no,northwest,5425.02335
62,male,26.695,0,yes,northeast,28101.33305
62,male,38.83,0,no,southeast,12981.3457
42,female,40.37,2,yes,southeast,43896.3763
31,male,25.935,1,no,northwest,4239.89265
61,male,33.535,0,no,northeast,13143.33665
42,female,32.87,0,no,northeast,7050.0213
51,male,30.03,1,no,southeast,9377.9047
23,female,24.225,2,no,northeast,22395.74424
52,male,38.6,2,no,southwest,10325.206
57,female,25.74,2,no,southeast,12629.1656
23,female,33.4,0,no,southwest,10795.93733
52,female,44.7,3,no,southwest,11411.685
50,male,30.97,3,no,northwest,10600.5483
18,female,31.92,0,no,northeast,2205.9808
18,female,36.85,0,no,southeast,1629.8335
21,female,25.8,0,no,southwest,2007.945
61,female,29.07,0,yes,northwest,29141.3603
 

三、模型構建

        我們定義六個維度X1到X6，分別代表age到region。其中給Xn設定一個βn作為模型變數。定義Y表示charges。

四、使用R語言求解模型

        我們先準備好insurance.csv資料檔案放入RStudio工作空間中。開啟RStudio。

        編輯程式碼如下：

insurance <- read.csv("insurance.csv", stringsAsFactors = TRUE)
str(insurance)

#既然因變數是charges,我們就來看一下它是如何分佈的
summary(insurance$charges)
hist(insurance$charges)

table(insurance$region)
cor(insurance[c("age","bmi","children","charges")])
pairs(insurance[c("age","bmi","children","charges")])

library("psych")
pairs.panels(insurance[c("age","bmi","children","charges")])

ins_model <- lm(charges ~ age + children + bmi + sex + smoker + region, data=insurance)
ins_model <- lm(charges ~ . , data=insurance)
ins_model
summary(ins_model)

insurance$age2 <- insurance$age^2
insurance$bmi30 <- ifelse(insurance$bmi >= 30, 1, 0)

ins_models <- lm(charges ~ age + age2 + children + bmi + sex + bmi30*smoker + region , data=insurance)
summary(ins_models)
 

五、程式碼分析

1、讀取檔案

         執行下方程式碼，讀取歷史資料檔案。

         insurance <- read.csv("insurance.csv", stringsAsFactors = TRUE)

        結果如下圖，我們已經將insurance.csv內容讀取到了變數insurance中。

2、轉換資料型別

        執行下方命令將insurance中資料轉換為因子型別。

        str(insurance)

        執行後結果如下

3、 分析報銷情況

        執行下方命令分析報銷情況

        summary(insurance$charges)

        執行後結果如下圖

        其中紅框所示為執行結果，其由左至右依次顯示最小值數、1/4位數、中位數、平均值、3/4位數、最大數。

4、檢視柱狀圖

        執行下方命令檢視柱狀圖

        hist(insurance$charges)

        執行後結果如下圖

        我們可以看到紅框所示為對報銷情況統計的柱狀圖。

5、檢視地區分佈

       執行下方命令，檢視地區分佈情況

        table(insurance$region)

        執行結果如下圖

       我們可以看出，東北、戲本、東南、西南人數樣本分佈還是比較均勻的。

6、求相關係數

        執行下方命令，檢視維度之間相關係數

        cor(insurance[c("age","bmi","children","charges")])

        執行結果如下圖

         從圖示表中可以看到年齡、肥胖係數、孩子數量、報銷費用之間的相關係數

7、獲取散點矩陣圖

        執行下方命令，檢視維度之間的散點矩陣圖

        pairs(insurance[c("age","bmi","children","charges")])

        執行結果如下圖

8、引入第三方軟體包，求解相關係數及其散點矩陣圖

        執行下方操作

        8.1、如下圖引入第三方軟體包

        8.2、執行下方命令

        library("psych")
        pairs.panels(insurance[c("age","bmi","children","charges")])

        簡單分析一下圖中資料，

        以左上到右下為中軸線，上半部分為各個維度之間的相關係數。相關係數越趨近於1代表越正相關，越趨近於-1代表越負相關，越趨近於0代表不相關。因此我們可以利用相關係數進行降維，將一些不相關的維度剔除。

8.3、執行下方命令

        ins_model <- lm(charges ~ age + children + bmi + sex + smoker + region, data=insurance)

        或

        ins_model <- lm(charges ~ . , data=insurance)
        得到下圖所示結果